Many therapeutically important natural products and pharmaceutical agents can be prepared from functionalized 1,2-dioxolane, cyclopentane, and tetrahydrofuran derivatives. The development of novel methodology for the efficient regio- and stereoselective syntheses of these ring systems is described. This methodology utilizes a radical-mediated addition of a two atom addend, such as molecular oxygen or a substituted alkene, across the carbon-carbon bond of a vinyl cyclopropane or vinyl oxirane to form the five-membered ring. Application of this chemistry to total syntheses of the antitumor antibiotic showdomycin and a portion of the antibiotic alborixin is planned.